# Static pressure

* In the design and operation of aircraft, static pressure is the air pressure in the aircraft’s static pressure system.

* In fluid dynamics, static pressure is the pressure at a nominated point in a fluid. Many authors use the term "static pressure" in place of "pressure" to avoid ambiguity.

* The term static pressure is also used by some authors in fluid statics.

Static pressure in design and operation of aircraft

An aircraft’s altimeter is operated by the static pressure system. An aircraft’s airspeed indicator is operated by the static pressure system and the pitot pressure system [Lombardo, D.A., "Aircraft Systems", 2nd edition – chapter 2] .

The static pressure system is open to the exterior of the aircraft to sense the pressure of the atmosphere at the altitude at which the aircraft is flying. This small opening is called the static port. In flight the air pressure is slightly different at different positions around the exterior of the aircraft. The aircraft designer must select the position of the static port carefully. There is no position on the exterior of an aircraft at which the air pressure, for all angles of attack, is identical to the atmospheric pressure at the altitude at which the aircraft is flying [”It is virtually impossible to find a position where the static pressure is always exactly the same as the pressure in the free airstream away from the aircraft”. Kermode, A.C., "Mechanics of Flight", 10th edition – page 65] . The difference in pressure causes a small error in the altitude indicated on the altimeter, and the airspeed indicated on the airspeed indicator. This error in indicated altitude and airspeed is called position error [Kermode, A.C.,"Mechanics of Flight", 10th Edition – page 65] [”Of these errors the error in detection of static pressure is generally the most serious and has the special name, "position error".” Dommasch, D.O., Sherby, S.S., and Connolly, T.F. (1967) "Airplane Aerodynamics", 4th edition – page 51, Pitman Publishing Corp., New York] .

When selecting the position for the static port, the aircraft designer’s objective is to ensure the pressure in the aircraft’s static pressure system is as close as possible to the atmospheric pressure at the altitude at which the aircraft is flying, across the operating range of weight and airspeed. Many authors describe the atmospheric pressure at the altitude at which the aircraft is flying as the "freestream static pressure". At least one author takes a different approach in order to avoid a need for the expression "freestream static pressure". Gracey has written “The static pressure is the atmospheric pressure at the flight level of the aircraft”. [Gracey, William, [http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19800015804_1980015804.pdf "Measurement of aircraft speed and altitude"] NASA, RP-1046, page 1] [Gracey, William, "Measurement of Aircraft Speed and Altitude", page 1] Gracey then refers to the air pressure at any point close to the aircraft as the "local static pressure".

Static pressure in fluid dynamics

The concept of pressure is central to the study of fluids. A pressure can be identified for every point in a body of fluid, regardless of whether the fluid is in motion or not. Pressure can be measured using an aneroid, Bourdon tube, mercury column, or various other methods.

The concepts of stagnation (or total) pressure and dynamic pressure arise from Bernoulli's equation and are significant in the study of all fluid flows. (These two pressures are not pressures in the usual sense - they cannot be measured using an aneroid, Bourdon tube or mercury column.) To avoid potential ambiguity when referring to pressure in fluid dynamics, many authors use the term static pressure to distinguish it from "total pressure" and "dynamic pressure". Static pressure is identical to pressure and can be identified for every point in a fluid flow field.

In "Aerodynamics", L.J. Clancy [Clancy, L.J., "Aerodynamics", page 21] writes: "To distinguish it from the total and dynamic pressures, the actual pressure of the fluid, which is associated not with its motion but with its state, is often referred to as the static pressure, but where the term pressure alone is used it refers to this static pressure."

Bernoulli's equation is fundamental to the dynamics of incompressible fluids. In many fluid flow situations of interest, changes in elevation are insignificant and can be ignored. With this simplification, Bernoulli’s equation for incompressible flows can be expressed as [Clancy, L.J., "Aerodynamics", equation 3.13] [Hurt, H.H. Jr, (1960), "Aerodynamics for Naval Aviators", page 9, A National Flightshop Reprint, Florida] [Anderson, J.D. Jr, "Fundamentals of Aerodynamics", 4th edition – page 212, McGraw-Hill, New York. ISBN 978-0-07-295046-5] :

$P + frac\left\{1\right\}\left\{2\right\} ho V^2 = P_0$

where:
$P$ is static pressure
$frac\left\{1\right\}\left\{2\right\} ho V^2$ is dynamic pressure, usually denoted by $q$
$P_0$ is total pressure which is constant along any streamline

Every point in a steadily flowing fluid, regardless of the fluid speed at that point, has its own static pressure $P$, dynamic pressure $q$, and total pressure $P_0$. Static pressure and dynamic pressure are likely to vary significantly throughout the fluid but total pressure is constant along each streamline. In irrotational flow, total pressure is the same on all streamlines and is therefore constant throughout the flow. [A.M. Kuethe and J.D. Schetzer (1959), "Foundations of Aerodynamics", Section 3.5 (2nd edition), John Wiley & Sons, Inc. New York ISBN 0 471 50952 3]

The simplified form of Bernoulli's equation can be summarised in the following memorable word equation [Clancy, L.J., "Aerodynamics", Section 3.5] [”The total pressure is composed of two parts, the static pressure and the dynamic pressure”. Streeter, V.L., "Fluid Mechanics" 4th edition – page 404] [ [http://www.grc.nasa.gov/WWW/K-12/airplane/bern.html NASA's guide to Bernoulli's Equation] ] :
:"static pressure + dynamic pressure = total pressure"

This simplified form of Bernoulli’s equation is fundamental to an understanding of the design and operation of ships, low speed aircraft, and airspeed indicators for low speed aircraft – aircraft whose maximum speed will be less than about 30% of the speed of sound.

As a consequence of the widespread understanding of the term "static pressure" in relation to Bernoulli’s equation, many authors [For example: Abbott, I.H. and Von Doenhoff, A.E. (1949) "Theory of Wing Sections", Navier-Stokes equations - section 5.4. Dover Publications, Inc., New York. Standard Book Number 486-60586-8] in the field of fluid dynamics also use "static pressure" rather than "pressure" in applications not directly related to Bernoulli’s equation.

The British Standards Institution, in its Standard [British Standard BS 185: Part 1: 1950 "Glossary of Aeronautical Terms"] "Glossary of Aeronautical Terms", gives the following definition:

"4412 Static pressure The pressure at a point on a body moving with the fluid."

Static pressure in fluid statics

The term static pressure is sometimes used in fluid statics to refer to the pressure of a fluid at a nominated depth in the fluid. In fluid statics the fluid is stationary everywhere and the concepts of dynamic pressure and total pressure are not applicable. Consequently there is little risk of ambiguity in using the term "pressure", but some authors [For example: "The pressure in cases where no motion is occurring is referred to as static pressure." Curtis D. Johnson, [http://zone.ni.com/devzone/cda/ph/p/id/190 Process Control Instrumentation Technology] , Prentice Hall (1997)] choose to use "static pressure" in some applications.

* Pitot-static system
* Stagnation pressure
* Dynamic pressure

References

Aircraft design and operation
* Citation
first = William
last = Gracey
editor-last =
editor-first =
contribution =
contribution-url =
title = Measurement of static pressure on aircraft
year = 1958
pages =
place = Langley Research Center
publisher = NACA
url = http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19930092348_1993092348.pdf
accessdate = 2008-04-26
doi =
id = TR-1364
.
* Citation
first = William
last = Gracey
editor-last =
editor-first =
contribution =
contribution-url =
title = Measurement of aircraft speed and altitude
year = 1980
pages =
place = Langley Research Center
publisher = NASA
url = http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19800015804_1980015804.pdf
accessdate = 2008-04-26
doi =
id = RP-1046
.
* cite book
last = Gracey
first = William
coauthors =
title = Measurement of Aircraft Speed and Altitude
publisher = John Wiley & Sons
date = 1981
location = New York
pages =
url =
doi =
id =
isbn = 0-471-08511-1

* Kermode, A.C. (1972) "Mechanics of Flight", Longman Group Limited, London ISBN 0-582-23740-8
* Lombardo, D.A., "Aircraft Systems", 2nd edition, McGraw-Hill (1999), New York ISBN 0-07-038605-6

Fluid dynamics
* Clancy, L.J. (1975), "Aerodynamics", Pitman Publishing Limited, London ISBN 0 273 01120 0
* Streeter, V.L. (1966), "Fluid Mechanics", McGraw-Hill, New York

Notes

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